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Ask a Physicist: The Shapiro Delay

Monday, February 01, 2016

Adhersh from India, wants to know:What will be the behavior of light when it passes between two highly massive bodies?Adhersh,Let’s elaborate a bit on your question, to make it into that most powerful of theoretical physics tools: a thought experiment!

Imagine we’re out in deep space—in spacesuits, of course—far from any gravitational influence, and illuminated only by the distant starlight. We’re far away from each other, but much, much farther from anything else.

At a certain exact time that we’ve agreed upon beforehand, I shine a laser pointer toward you, aiming precisely at a light-sensitive panel (like a solar panel, which converts light into an electrical signal) installed on your suit. When the laser light strikes this solar panel, a computer in the suit notes that it’s received a signal and the time that it received it—finding that it was a precise seven seconds after the time we agreed I would send the signal.

Since the light signal took seven seconds to get from me to you, we can deduce that you and I are some 2.1 billion meters—or seven “light-seconds”—apart.

Light-seconds is a measure of distance, like light-years: since the speed of light isconstant, it's often convenient to talk about astronomical distances in terms of howlong it would take a ray of light to make the journey.

Now, imagine the same scenario, but instead of us being alone there are two massive objects between us—equidistant from the path the laser will take, as shown below:

If just one of those objects were there, it would deflect the laser beam to one side in a process called gravitational lensing, and the signal would never reach you at all, landing somewhere among the distant stars! With both bodies the same mass and same distance from the laser's trajectory, however, it takes the same path it originally would have, and reaches you just the same—or does it?

When the agreed-upon time comes, I send my laser signal shooting through the gap between these two planets, across a few billion meters of space, to the photoreceptor panel in your suit. When the light hits it, a computer in your suit records that, just as before, it's received a signal. Unlike before, however, it notes that it was slightly MORE than seven seconds between when the signal was sent and when it was received! This strange time-warping phenomenon is called the Shapiro Delay.

How can this be? There are two ways to interpret it: the most intuitively obvious is that a change in gravitational potential—going from "high" to "low" to "high" again, the way it would as it approaches and then leaves the vicinity of those massive bodies—slows down light. Light moves slower than c all the time—whenever it's traveling through anything other than the vacuum of space. However, one of the fundamental assumptions of modern physics is that the speed of light in a vacuum is constant, regardless of what it's around. To get around this when trying to work out the math of how prominent this effect should be, it's instead assumed that time itself is slowed down by this change.

(Note: this is different from ordinary gravitational time dilation, where clocks tick faster the closer they are to a massive object—since our signal is starting and ending at the same gravitational potential, we shouldn't see any unusual redshift or blueshift, as we'd get from gravitational time dilation.)

But time, as we've discussed before, is just a construct—a way of ordering events. To those who can stretch their imaginations into the fourth dimension and embrace "timeless physics", this scenario can be seen another way—as a warping of space.

You've probably seen the "elastic sheet" model of gravity, demonstrating the way mass warps spacetime. While the analogy isn't perfect, it provides an interesting insight here. In the first image above, where there's no appreciable mass, the light ray takes a straight path from me to you, and takes seven seconds to make the trip. In the second image, you can imagine the fabric of spacetime being bent "down" into the page by the gravity of the massive bodies. Suddenly, the straightest path from me to you bends into the third dimension, meaning a photon would have to travel "downhill" and back "up" to make it to its destination. Even if it were moving at a constant speed, it would still take longer to make the trip, because it's actually traveling a greater distance.

The really neat thing about all this is that you can think of the situation either way—as a stretching of either space or time. Since your question happens in three-dimensional space rather than the 2D example above, it might be hard to imagine a fourth spatial dimension to "stretch" things into, and this is where time comes in very handy—you can simply imagine treat time as the fourth dimension and imagine that it's being stretched by the gravity of these planets. Equivalently, if your mind's eye is up to the task, you can imagine that there's a literal fourth spatial direction—perpendicular to the three in which we seem to exist—and that space is being stretched into it, giving the light a longer path to travel.

This equivalence is one of the more mind-bending properties of relativity theory, and it's part of why physicists use the term "spacetime" when they're talking about the fabric of the universe—space and time, when you get to the nitty-gritty of it, behave in such a way that it doesn't really make sense to talk about one without the other.

This is an extremely insightful question, Adhersh—it cuts to the heart of one of the fundamental tests of Einstein’s theory of general relativity, and helps get at the deeper meaning of one of modern physics’ most crucial assumptions. The fact that you’re wondering about things like this bodes well for your future in physics!